1. Field of the Invention
The present invention relates to an apparatus for measuring power distribution in the core of a nuclear reactor.
2. Description of the Prior Art
To know power distribution in the core of a nuclear reactor is a matter of importance in the operation of the nuclear reactor. There have so far been proposed some types of apparatuses for measuring the power distribution. A first type of the measuring apparatus is of such an arrangement that a large number of stationary small neutron detectors are disposed within the nuclear reactor. In this first type of measuring apparatus, it is essential that the large number of neutron detectors will stably operate for a long period of time. It, however, is very difficult to manufacture such reliable and stable neutron detectors.
A second type is of such an arrangement that a large number of holes for insertion of a small neutron detector are made in the nuclear reactor and a small neutron detector is inserted into these holes one after another so that it scan and measure the power distribution in the core. In the case of this second type of measuring apparatus, such problems are encountered that a long time is taken for measuring the output distribution in the nuclear reactor in its entirety and, when the power distribution in the core changes abruptly, the apparatus is unable to follow the abrupt changes.
As a third type of the measuring apparatus, there is one as disclosed in Japanese Laid-open Patent Publication No. 52-107496. The apparatus of this type uses a number of small size detectors provided by cutting a detector of an out-of-core neutron measuring apparatus, which has been conventionally in use for measuring output power of a pressurized water reactor, across its axis into segments and is adapted to obtain the power distribution in the core along its axis through calculation of output signals of the small size detectors.
The principle of the third type measuring apparatus will be described with reference to the drawings hereunder. FIG. 1 is a schematic arrangement diagram showing arrangement of a nuclear reactor and a neutron detector. Referring to the figure, 10 denotes a reactor core and 20 denotes a neutron detector, which is formed of small size detectors 21-24 provided by cutting the neutron detector 20 across its axis (into four segments in the present case).
FIG. 2 shows relationship between reactor power axial distribution P(Z) and the output signals D.sub.k of the small size detectors 21-24 shown in FIG. 1. Since each of the small size detectors 21-24 is affected most strongly by the power of the portion of the core 10 of the nuclear reactor closest thereto, the pattern formed by the magnitude of each of the output signals D.sub.k of the small size detectors 21-24 becomes similar to the reactor power axial distribution P(Z).
FIG. 3 is a diagram for explaining the method for obtaining, by calculation, the reactor power axial distribution P(Z) from the output signals D.sub.k of each of the divided small size detectors 21-24. Here is taken the point of view that the reactor power axial distribution P(Z) is approximated by Fourier series as ##EQU1## where H: the maximum height in the core.
If C.sub.i in the expression (1) can be obtained from the output signals D.sub.k of the small size detectors 21-24, then the power distribution in the core can be obtained from the output signals of the out-of-core neutron detector 20 within the accuracy of the approximation of the expression (1).
By dividing the height of the core into the same number as that of the small size detectors 21-24 and integrating (1) on each interval, the integrated value P.sub.j on the jth interval from the bottom will be expressed as ##EQU2## where
B.sub.j : the lower limit of the jth interval from the bottom,
T.sub.j : the upper limit of the jth interval from the bottom.
By defining ##EQU3## the integrated values P.sub.j of the reactor power on each interval will be expressed by use of the matrix [Q.sub.ji ] as EQU [P.sub.j ]=[Q.sub.ji ] [C.sub.i ] (4)
hence EQU [C.sub.i ]=[Q.sub.ji ].sup.-1 [P.sub.j ] (4)'
If the relationship between the output signals D.sub.k of each of the small size detectors 21-24 and the integrated values P.sub.j of the reactor power on each interval can be determined, C.sub.i can be determined from the output signals D.sub.k of each of the small size detectors 21-24, and hence the approximate value of the reactor power distribution P(Z) will be obtained from the expression (1).
Further, it is considered that the output signals D.sub.k can be expressed as a linear combination of the power output from each of the sections of the core and the transformation matrix therefor is virtually invariable for a specific nuclear reactor. Hence, letting [A.sub.kj ] be a constant matrix, we obtain EQU [D.sub.k ]=[A.sub.kj ] [P.sub.j ] (5)
hence EQU [P.sub.j ]=[A.sub.kj ].sup.-1 [D.sub.k ] (5)'
Since, the transformation matrix [A.sub.kj ].sup.- is dependent on the structure of the nuclear reactor, it must be obtained from actual measurement data of the nuclear reactor.
In other words, it is required that a number of sets of data of the integrated values P.sub.j of the reactor power on each interval and the detector outputs D.sub.k are obtained through simultaneous measurement on the nuclear reactor to which the present method is desired to be applied. The integrated values P.sub.j of the reactor power on each interval can be obtained by integrating, on each interval, the reactor power axial distribution P(Z) obtained from the incore neutron instrumentation.
The transformation matrix [A.sub.kj ].sup.-1 is obtained by solving simultaneous equations provided by these data. The obtaining of the transformation matrix [A.sub.kj ].sup.-1 constitutes initial calibration on S/W in the present method. Once the transformation matrix [A.sub.kj ].sup.-1 is determined, the reactor power axial distribution P(Z) can be obtained from the output signals D.sub.k of the small size detectors 21-24 within the limit of the accuracy of the approximation of the expression (1).
Here, the sets of data used in the present method, namely, the integrated values P.sub.j of the reactor power on each interval and the detector outputs D.sub.k must be such that correspond to various power distribution and also the number of sets of the data must at least be equal to the number of division of the neutron detector 20 (four in the present case) or above.
Since the prior art apparatus for measuring the nuclear reactor power distribution has been structured as described above, it is really difficult to obtain the data for finding the transformation matrix [A.sub.kj ].sup.-1 at the stage of the initial calibration. The data satisfying the aforementioned conditions are normally obtained only from the plant at the stage before commencement of commercial operation when various tests are carried out. Unless the used data fully satisfy these conditions, it becomes very difficult to obtain the transformation matrix [A.sub.kj ].sup.-1 and the accuracy of the obtained transformation matrix [A.sub.kj ].sup.-1 becomes very low. The prior art apparatus have had these problems.